On different models of representations of the infinite symmetric group

• Published in: Advances in applied mathematics Vol. 37; no. 4; pp. 526 - 540
• Main Authors: Tsilevich, N.V., Vershik, A.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2006
• ISSN: 0196-8858; 1090-2074
• DOI: 10.1016/j.aam.2005.09.007

We present an explicit description of the isomorphism between two models of finite factor representations of the infinite symmetric group: the tableau model in the space of functions on Young bitableaux and the dynamical model in the space of functions on pairs of Bernoulli sequences. The main tool used is the Fourier transform on the symmetric groups. We also start the investigation of the so-called tensor model of two-row representations of the symmetric groups, which plays an intermediate role between the tableau and dynamical models, and show its relations to both these models.